This project's core goal is to enhance understanding of change processes in children's thinking. Overlapping-waves theory is central to this effort. It postulates that children (and adults) typically possess multiple ways of thinking about a given phenomenon; that development involves both changes in the relative frequencies of existing ways of thinking and introduction of new ways of thinking; that children choose adaptively among alternative ways of thinking from early in learning; that choices become increasingly adaptive with experience; and that generation of new ways of thinking is constrained by domain-specific conceptual knowledge. Microgenetic methods are used to densely sample changing behavior as it is changing, typically on a trial-by-trial level. These methods allow identification of when new strategies are first used. This, in turn, allows examination of what led up to the discovery and how it was generalized beyond its initial use. The goals for the next 5 years are to 1) Establish the applicability of overlapping waves theory to early development; 2) Understand developmental differences in learning; 3) Examine the roles of unconscious and conscious processes in children's discovery of new strategies; 4) Describe how strategy choices become increasingly adaptive with experience. 5) Formulate general models of strategy choice and strategy discovery. The work promises to be of educational as well as theoretical importance, due both to the tasks being studied (mathematical and scientific problem solving) and the topics being investigated (ways to promote insights, sources of individual differences in learning; readiness to learn, etc.)